I would say those are decent points, with the exception that I would say, at least in the American system which I am familiar with, with the advancement of technology like DNA testing, and the high standard of guilt, the odds of a man today being Innocent yet sentenced to death are very small, without a doubt the smallest they’ve been in history. I don’t think the chance of a man being wrongly sentenced in the past should have bearing on what we do today.
But where I differ is I don’t think the primary purpose of punishment is included on your list, being administering justice.
Of all the moral laws God gives, the vast majority are centered around the sanctity and dignity of human life, and that as such the will full destruction of it needs to be met with the ultimate punishment. God declares to Noah that even a beast who kills a human needs to pay with it’s life (Gen 9:5) and reiterates this when giving the ten commandments at Sinai (ex 21:28). Obviously there is no such thing as redeeming an ox or a lion. It seems to me just a matter of justice.
And although death is permanent, having a date put over your head is a very sobering thing that drives many many people to repent. Though obviously not an infallible source, Aquinas wrote to the effect that if a man is faced with his own death, and this doesn’t spur his heart to repent his crime and draw away from cruelty, it’s very possible that nothing could inspire him to do so. I think that’s a pretty compelling argument.
If the Catechism said the death penalty was explicitly always evil, I might be saying something different.